those months are great for southern Africa, although in June it might be crisp at night when travelling through the central highveld (Johannesburg down to Colesburg). he Natal coast is fine in winter. So why return to Cape Town and not ship the bike from Durban instead? Cape Town does have fine days in winter, but often rain and strong winds.
my suggestion would be not to travel down to Cape Town all the way along the coast. It gets boring after a while... A great trip would be to ake the bee-line to northern Lesotho, enter somewhere near Oxbow, take the road to Mokhotlong and further to the Sani Pass. Then head north-east to St. Lucia, ride along the coast right up to Coffee Bay in the Transkei. If possible don't take the N2, rather take the side roads.
From Coffee Bay pay a visit to the Addo Elephant Park, after that travel through Baviaans Kloof. Beautiful off-road, brilliant landscape.
Further west is the Swartberg mountain range and the Swartberg Pass, take the Route 62.
These are a few alternatives to the rather boring Garden Route.
Only when we pause to wonder
do we go beyond the limits of our little lives.